Arnold Dreyblatt

from Arnold Dreyblatt: Tuning Systems Explanation, www.dreyblatt.net/html/music.php?id=67

The Dreyblatt Tuning System is calculated from the third, fifth, seventh, ninth and eleventh overtones and their multiples in the following pattern:

1	3	5	7	9	11
3	9	15	21	27	33
5	15	25	35	45	55
7	21	35	49	63	77
9	27	45	63	81	99
11	33	55	77	99	121

These mathematically related overtones are heard as tonal relationships when they are transposed and sounded above a fundamental tone. In this process of transposition from their position in the natural overtone series, these tones fall (unequally) in the span of one octave in the following order:

1, 33, 35, 9, 77, 5, 81, 21, [11,] 45, 3, 49, 99, 25, 27, 55, 7, 15, 121, 63, (2)

These tones are performed in "just intonation' based on a fundamental tone of "F".

Note	Freq.	Partial	Cents
F	349.2	1	0
F#	360.11	33	-47
G	381.93	35	-45
G#	392.85	9	+4
G#	420.13	77	+20
A	436.5	5	-14
A	441.95	81	+8
A#	458.32	21	-29
B	480.15	11	-49
B	491.06	45	-10
C	523.8	3	+2
C	534.71	49	+38
C#	540.16	99	-45
C#	545.62	25	-28
D	589.27	27	+6
D	600.18	55	+37
D#	611.1	7	-31
E	654.75	15	-12
E	660.20	121	+2
F	687.48	63	-27